A landscape architect is designing a section of a path. The elevation h h\,h of the path (in meters) relative to a reference level is modeled by the function
h(x)=112x4+sinx+5 h(x) = \frac{1}{12}x^4 + \sin x + 5 h(x)=121x4+sinx+5for −π≤x≤π-\pi \le x \le \pi−π≤x≤π, where x x\,x represents the horizontal distance in meters from a marker.
Determine whether the curve with equation y=h(x)y = h(x)y=h(x) has a point of inflection at the point where x=0x = 0x=0. Fully justify your answer.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
